Consider a body of mass 1.0 k g at rest at the origin at time t = 0 . A force F → = α t i ^ + β j ^ is applied on the body, where α = 1.0 N s - 1 a n d β = 1.0 N . The torque acting on the body about the origin at time = 1.0 s i s τ → . Which of the following statements is (are) true?

Step-by-step solution

F → = α t i ^ + β j ^ a t t = 0 , v = 0 , r → = 0 → α = 1 , β = 1 F → = t i ^ + j ^ m d v → d t = t i ^ + j ^ On integrating m v → = t 2 2 i ^ + t j ^ m = 1 k g d v → d t t 2 2 i ^ + t j ^ r → = 0 → a t t = 0 On integrating r → = t 3 6 i ^ + t 2 2 j ^ τ → = - 1 3 k ^ v → = t 2 2 i ^ + t j ^ At t = 1 v → = 1 2 i ^ + j ^ = 1 2 i ^ + 2 j ^ m / s e c At t = 1 s → = r 1 → - r 0 → = 1 6 i ^ + 1 2 j ^ - 0 → s → = 1 6 i ^ + 1 2 j ^ s → = 1 6 2 + 1 2 2 = 10 6 m